Are fuel system cleaners (like Gumout) worth using regularly?
Unless you've got an extraordinary circumstance or legitimate reason for using it, don't. Chances are the usage will temporary make the symptoms subside, only to return again later.
The way I see it, if your vehicle required it you would find it listed in the recommended maintenance items list in your owner's manual.
I think another side to this question is first you need to answer how old is the vehicle, how many miles on it, have you had it regularly maintained (why do you need the cleaner in the first place)?
So back to my first point, if you desperately need to try it, go for it, otherwise figure out what your issue really is before dumping chemicals into your gas tank.
Although this isn't a scientific test, from experience I've found that using Gumout or Berrymans B-12 (which is much cheaper but very effective) every 3,000 miles has been fairly effective at keeping my engine cleaner.
I've confirmed this because last year when changing the oil on my fathers car, I decided to run SeaFoam (another excellent fuel system cleaner -- although it's $9 a can so I save it for oil change time) through my father's Ford Thunderbird intake. It's a fairly common use of Seafoam as it's a pretty simple DIY thorough cleaning of your car's fuel system which is much more thorough than just adding the fluid through the fuel tank.
After adding the Seafoam, I ran the car for a test drive and literally a massive plume of smoke was shooting out of the car's exhaust like it was a drag racer. The smoke actually was all of the gunk in the fuel intake system, which was being removed by the SeaFoam.
Now, after doing the Thunderbird, I did the same procedure on my Toyota Avalon which I've been adding Gumout or B-12 (depends on what's on sale) every 3,000 miles and when I did the Seafoam run, after a small plume of smoke for a few seconds, my car's exhaust literally was clean.
Now, your mileage might vary based on your driving style and car type, however at the least have a look at Seafoam because it's used all the time for the crankshaft, fuel intake, and fuel system -- and on virtually all car forums that's the cleaner of choice.
For routine (every 3,000 miles) cleanings, I'd just add a can of Berrymans B-12 (usually costs $3 a can) or go with Gumout if it's on sale. Just make sure it's the fuel system cleaner and not fuel injector cleaner as the latter allows deposits to build up after adding it.
Still, despite the success story, I will point out that if you're having fuel system problems of a serious nature (i.e. the check engine light, misfiring, very clogged injectors, etc) going to a mechanic is a must.